Response variable

The response variable is the outcome the analysis is trying to account for, also called the dependent variable. It supplies the $y$ values, sits on the vertical axis, and is what a fitted model predicts, which is why $\hat{y}$ (y-hat) and every residual are measured in the response's units and never in the explanatory variable's. In an experiment it is what you measure after a treatment has been applied.

A nursery fits $\hat{y} = 12 + 0.6x$, where $x$ is grams of fertilizer and $y$ is plant height in centimeters. A plot given 30 grams has predicted height $12 + 0.6(30) = 30$ centimeters. That plant actually measures 27, so its residual is $27 - 30 = -3$ centimeters: three centimeters short, in the response's units, measured vertically.

The wrong sentence is "the response variable goes up 0.6 centimeters for every extra gram." A variable does not go up. At each amount of fertilizer the response has a whole spread of possible heights, and the fitted line traces the mean of those, so what rises by 0.6 is a predicted mean and not any plant; the residual above is one plant's departure from it. Time order does not assign the role either. The response is whichever variable the question is trying to account for, not whichever you happened to measure second.

The response does not have to be numerical. If what you record is whether a patient recovered, yes or no, the response is categorical and the summary is a proportion rather than a mean, which puts the analysis in Unit 3 rather than Unit 5. What stays the same either way is the direction of the question, since the response is the variable being explained.

Linear regression models are topic 5.3 and residuals are 5.4. The two roles are laid out together at explanatory vs response variable.